WASHINGTON - President Barack Obama may be half right when he says America and Russia, at odds over Syria and Ukraine, are not diplomatic grandmasters squaring off on a Cold War-style chessboard.

The White House, struggling to contain multiple global crises, has no incentive to ignite the foreign policy nightmare a wider confrontation with Moscow would entail.

But there is growing, if belated, recognition in Washington that President Vladimir Putin sees foreign policy primarily through of lens of restoring faded post-Soviet clout -- and that any loss of US influence furthers that goal.

Past American support for NATO expansion -- and for the right of ex-Soviet states to determine their own path -- is seen in Washington as simply standing up for peoples that share its core value of freedom.

But some officials and analysts realize that in Moscow, such a stance is often seen, or portrayed, as an attempt to seed US influence in what Russia sees as its own orbit.

Still, the Obama administration seeks to preserve Russian cooperation where it can, on Iran nuclear talks, on extricating US troops and material from Afghanistan and on counter-terrorism.

But frustrated by Russian behavior, Washington is making increasingly clear it rejects the core argument of Kremlin foreign policy -- the idea that Russia is entitled to restore its Soviet-era sway.

"We consider this idea of spheres of influence to be a wildly outmoded notion," said a senior State Department official on condition of anonymity.

"We've been clear about that with the people of Ukraine, we've been clear about that with Russia."

Relations between Putin and the Obama administration have deteriorated for months -- the showdown over Ukraine's relationship with Europe is simply the latest flashpoint.

Obama aides also vent at Russia's support for President Bashar al-Assad, which it faults for thwarting diplomatic efforts to end Syria's civil war.

"Russia needs to be a part of the solution and not be distributing so much more weapons and so much more aid that they're in fact enabling Assad to double-down," said Secretary of State John Kerry on Monday.

Putin's decision to harbor fugitive US intelligence leaker Edward Snowden, which carried the whiff of his KGB past, caused Obama to abort a planned summit last year.

But letting US-Russia relations further shred is also not an option.

This is one reason why the administration highlights its deal with Russia requiring Assad to destroy chemical weapons last year -- even if it is well behind schedule.

"It behooves the administration to recognize that we are going to need the Russian partnership in terms of Iran, counter-terrorism and in many areas," said Matthew Rojansky, a Russia expert at the Wilson Center.

But forging a policy to deal with Putin who seems determined to thwart Washington, is complicated.

Each dispute, whether over Syria or Ukraine, exposes Obama to claims he is weak and inconsistent, from domestic foes who saw his earlier "reset" of ties with Moscow as a pipe dream.

"I don't think there's a competition between the United States and Russia," Obama said in Mexico on Wednesday.

"Mr Putin has a different view on many ... issues. I don't think that there's any secret on that.

"Our approach as the United States is not to see these as some Cold War chessboard in which we're in competition with Russia."

Obama had originally hoped to work with Putin, when he returned as president in 2012 -- famously telling then Russian leader Dmitry Medvedev he could be more "flexible" over a row over a US missile defense shield after his own reelection the same year.

But Putin snuffed out the "reset" under which Medvedev and Obama sealed a nuclear arms treaty, tightened sanctions on Iran and ate lunch together at "Ray's Hell Burger" a restaurant a few miles from the White House.

- Things started badly and went downhill -

Putin started out by snubbing a G8 summit at Camp David, and things went downhill from there.

But while they may be at odds over Syria and Ukraine, both former Soviet client states, Washington and Moscow have yet to split over Iran -- and that may be key to Obama's policy stance.

Russia and the United States are members of the P5 plus one grouping of world powers negotiating with Tehran over its nuclear weapons program.

A deal to thwart an Iranian bomb would be the prime achievement of Obama's second term -- and would likely be impossible without Russia's help.

Washington might be outraged when it sees human rights crushed when Ukrainian troops fire on protesters in Kiev -- and will likely impose sanctions as a result.

But no one is arguing the showdown is a dominant national interest.

In Ukraine, "the stakes for Russia are simply far higher than for the United States, as much as we profess deep concern," Rojansky said.